\;{1}{{1+x}} is equal to

Correct Answer is : 2(1+x)12+K2(1+x)¹/2}+K2(1+x)21+K

Correct Answer is : 2(1+x)12+K2(1+x)¹/2}+K2(1+x)21+K

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Integral Calculus

Question : 47 of 73

Marks: +1, -0

\int\;\frac{1}{\sqrt{1+x}}

is equal to

Solution:

Concept:

The integral is a standard power rule after substitution.

Explanation:

Let

u = 1 + x

. Then

du = dx

The integral becomes

\int \frac{1}{\sqrt{u}} \, du = \int u^{-1/2} \, du

Using the power rule,

\int u^n \, du = \frac{u^{n+1}}{n+1} + C

for

n \neq -1

, we get

\frac{u^{1/2}}{1/2} + C = 2u^{1/2} + C = 2(1+x)^{1/2} + C

Thus, the integral equals

2(1+x)^{1/2} + K

Answer:

2(1+x)^{\frac{1}{2}}+K

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